A new Korteweg-de Vries equation-based sub-equation method and its application to the (2Â +Â 1)-dimensional Korteweg-de Vries equation

With the help of the symbolic computation system Maple, we present Korteweg-de Vries equation-based sub-equation method. Being concise and straightforward, it is applied to the (2 + 1)-dimensional Korteweg-de Vries equation. It is shown that N-soliton solution of the (2 + 1)-dimensional Korteweg-de Vries equation can be found by this new method. The method can be applied to other nonlinear partial differential equations in mathematical physics.